A recent experiment at the European Laboratory for Non-Linear Spectroscopy (LENS) on a three-dimensional (3D) Fermi gas has reported a negative effective mass ($m^{*}<0$) for Fermi polarons in the strongly repulsive regime. There naturally arises a question of whether the negative $m^{*}$ is a precursor of the instability towards phase separation (or itinerant ferromagnetism). In this paper, we make use of the exact solutions to study the ground state and excitation properties of repulsive Fermi polarons in one dimension, which also can exhibit a negative $m^{*}$ in the super-Tonks-Girardeau regime. By analyzing the total spin, quasimomentum distribution, and pair correlations, we conclude that the negative $m^{*}$ is irrelevant to the instability towards ferromagnetism or phase separation but rather an intrinsic feature of collective excitations for fermions in the strongly repulsive regime. Surprisingly, for large and negative $m^{*}$, such an excitation is accompanied with a spin-density modulation when the majority fermions move closer to the impurity rather than being repelled far away, contrary to the picture of phase separation. These results shed light on the recent observation of negative $m^{*}$ in the 3D repulsive Fermi polarons.

• Received 4 August 2017

DOI:https://doi.org/10.1103/PhysRevA.96.053609